$75$ people attended a baseball game. Everyone there was a fan of either the home team or the away team. The number of home team fans was $49$ less than $3$ times the number of away team fans. How many home team and away team fans attended the game?
Answer: Let $x$ equal the number of home team fans and $y$ equal the number of away team fans. The system of equations is then: ${x+y = 75}$ ${x = 3y-49}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${3y-49}$ for $x$ in the first equation. ${(3y-49)}{+ y = 75}$ Simplify and solve for $y$ $ 3y-49 + y = 75 $ $ 4y-49 = 75 $ $ 4y = 124 $ $ y = \dfrac{124}{4} $ ${y = 31}$ Now that you know ${y = 31}$ , plug it back into ${x = 3y-49}$ to find $x$ ${x = 3}{(31)}{ - 49}$ $x = 93 - 49$ ${x = 44}$ You can also plug ${y = 31}$ into ${x+y = 75}$ and get the same answer for $x$ ${x + }{(31)}{= 75}$ ${x = 44}$ There were $44$ home team fans and $31$ away team fans.